This paper discusses finite automata regulated by control languages over
their states and transition rules. It proves that under both
regulations, regular-controlled finite automata and
context-free-controlled finite automata characterize the family of
regular languages and the family of context-free languages,
respectively. It also establishes conditions under which any
state-controlled finite automaton can be turned into an equivalent
transition-controlled finite automaton and vice versa. The paper also
demonstrates a close relation between these automata and programmed
grammars. Indeed, it proves that finite automata controlled by languages
generated by propagating programmed grammars with appearance checking
are computationally complete. In fact, it demonstrates that this
computational completeness holds even in terms of these automata with a
reduced number of states.